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Interspecies Correlation of the Pharmacokinetics of Erythromycin, Oleandomycin, and Tylosin
Interspecies Correlation of the Pharmacokinetics of Erythromycin, Oleandomycin, and Tylosin GWENS. DUTHU Received December 20, 1984,from Pfizer, Inc., Central Research, Groton, CT 06340. Abstract 0 Knowledge of the disposition of macrolides in a single animal species has been insufficient for the prediction of the pharmacokinetics of macrolides in humans. To better understand the species
differences in the pharmacokineticsof macrolide antibiotics, the disposition of erythromycin, oleandomycin, and tylosin in several mammalian species was examined. Generally, the serum concentration versus time profiles of these drugs after intravenous administration were described by two-compartment kinetic models and were similar within each species. These drugs were rapidly cleared, resulting in terminal halflives of <2 h. Comparison of their pharmacokinetics showed greater variation in antibiotic disposition among animal species than noted for the differences within a species. When the pharmacokinetic data was fitted to an allometric model, the logarithms of volume of distribution, clearance, and half-life were linearly related to the logarithms of body weight. From these relationships, the human pharmacokinetics of erythromycin and oleandomycinwere extrapolated and found to approximate observed human pharmacokinetics.
The disposition of erythromycin, the most frequently prescribed macrolide antibiotic used in the treatment of infections, has been well studied in humans,' whereas the disposition of other macrolides has been less well characterized. In humans, erythromycin is widely distributed in tissues1 and actively cleared by the liverZwith only 10-15% of the drug excreted by the kidney^.^ The disposition of macrolides in animals appear to be similar in that wide tissue distribution and biliary excretion have been rep0rted.M However, there are few comparative studies of the pharmacokinetics of erythromycin and related macrolides.7-9 Furthermore, interpretation of these studies has been complicated by the gastric instability, variable absorption, and variable protein binding of these drugs.10.11 Three macrolide antibiotics were chosen for this comparative study: the 14-membered ring antibiotics erythromycin and oleandomycin and the 16-membered ring antibiotic tylosin. The intraspecies and interspecies differences in pharmacokinetics were determined for these compounds in several animal species. Interspecies differences in pharmacokinetics are due to physical processes (such as blood flow and organ clearances) and metabolic processes.12 The physical processes can vary predictably among mammalian species, independent of metabolic processes.13 When interspecies differences in pharmacokinetics are treated as a function of body size,lPl7 species differences in drug metabolism are ignored and instead empirical scaling functions are used.18 Not only has no single species been able to predict the pharmacokinetics of macrolides in humans but the relative ranking of macrolides based on these parameters is species dependent. In an effort to more accurately estimate human pharmacokinetics from animal data, the allometric mode119 was used. The results suggest that the allometric model may be a valid part of the methodological paradigm for the prediction of human pharmacokinetics of macrolide antibiotics.
Experimental Section Intravenous Protocol-Macrolide antibiotics were administered intravenously to animals, and blood samples were collected at OO22-3~9/85/0900-0943$0 1.OO/O 0 1985, American Pharmaceutical Association
Accepted for publication May 10, 1985.
appropriate times. Male mice were dosed with erythromycin or oleandomycin at 10 mglkg. Two animals per time point were sacrificed at 0, 1,3,5, 10, 15,30,60,90,and 120 min postdose. Blood was collected and serum was prepared; the serum was assayed for the drug by microbiological assay.20 Male Sprague-Dawley rats were dosed a t 25 m g k g with erythromycin, oleandomycin,. or tylosin. Blood samples were drawn from the orbital sinus at 0,0.25,0.5,1,2, 4,and 6 h postdose. Serum was prepared and analyzed for the drug by an HPLC procedure.21 Male New Zealand White rabbits were dosed at 10 mg/kg with erythromycin. Blood was collected from the ear vein at 0, 0.25,0.5, 1, 2, 4,and 6 h postdose and serum was prepared; the serum was analyzed for the drug by HPLC. Male and female beagle dogs were dosed at 10 mglkg with erythromycin or oleandomycin; blood was drawn from the jugular vein at 0,0.25,0.5, and 24 h postdose. Serum was prepared and analyzed for 1,2,3,4,6, the drug by HPLC. Pharmacokinetic Analysis-Serum concentrations of drug were analyzed by model-independent and model-dependent pharmacokinetic methods. The area under the serum concentration versus time curve from time zero to infinity (AUC) was calculated by the trapezoidal method for AUCo-,, and by adding the extrapolated area from time t to infinity (drug concentration at tlterminal slope). The area under the first moment of the serum concentration versus time curve (AUMC)was used to calculate volume of distribution at steady state (Vd,,) according to the equation:22
Vd,,
=
(dose x AUMC)/AUC2
The terminal half-life was obtained from the log-linear leastsquares fit of the terminal portion of the serum concentration versus time curves (2-4 data points). Systemic clearance was determined by clearance = doselAUC. For compartmental analysis and estimates of initial serum concentrations (Co),the serum concentration data was fitted by computer using NONLIN. Allometric Analysis-The volume of distribution, clearance, and terminal half-life (pharmacokinetic parameters, PK) were logarithmically transformed and plotted as a function of the logarithm of the body weight. The data from the linear regression analysis was used in the allometric equation PK = aBb,where a is the y-intercept, B is the body weight in grams, and b is the slope of the log-log plot.'* The empirically determined coefficients and exponents were used t o estimate human pharmacokinetic parameters. A body weight of 7 x lo4 g was used for the human body weight.
Results The pharmacokinetic parameters which describe the kinetics of erythromycin in mice, rats, rabbits, and dogs are presented in Table I. Erythromycin showed a biphasic exponential decline in serum concentrations. The Vd,, ranged Table I-Pharmacokinetics of Erythromycin After an Intravenous Dose to Mice, Rats, Rabbits, and Dogs
Mouse
Rat
Rabbit
Dog
(10 mg/kg)
(25mg/kg)
(10 mg/kg)
(10 mg/kg)
7.8 39 3.6 77
3.5 76 9.3 73
2.5 84 6.8 53
10.6 103 2.7 21
Kinetic Parameter
Gl (MlmL)B t,, (min) vd, (Ukg)
CL (mUmin/kg) a
Serum concentration immediately after intravenous bolus injection. Journal of Pharmaceutical Sciences 1943 Vol. 74, No. 9, September 1985
from 2.7 to 9.3 L/kg and the half-life increased, while clearance decreased with increasing species body weight. Dogs had the highest initial serum concentration of drug (CO) after intravenous dosing. Like erythromycin, oleandomycin exhibited biphasic kinetics with similar relationships among the pharmacokinetic parameters (Table 11): Vd,, was 1.6-6.8 L/kg and clearance rates decreased and terminal half-lives increased with increasing species body weight. The dog was again notable for high Co values. Tylosin, in contrast to erythromycin and oleandomycin, decreased monoexponentially in the rat, with the shortest half-life, highest clearance rate, and smallest Vd,, of the three macrolides in the rat (Table 11). Table I11 summarizes the pharmacokinetic data reported in the literature or by this laboratory for erythromycin, oleandomycin, and tylosin. Large volumes of distribution (greater than the body volume) were observed for all three macrolides in the dog and smaller species; for humans and cows, the Vd,, values were less than their respective body volumes. Clearance rates for the three macrolides were comparable to hepatic blood flow in the mouse, rat, and rabbit but were considerably lower in the dog, human, and cow. The three smaller animal species also had shorter terminal half-lives (<2 h). Differences in the volumes of distribution, clearances, and half-lives within a n animal species for the three antibiotics (intraspecies differences) and differences across species for each antibiotic (interspecies differences) were compared. The intraspecies differences were less than threefold, whereas the interspecies differences varied as much as 10-fold (Table 111).The interspecies differences appeared to be generally related to body weight: as body weight increased, the terminal half-life increased and the volume of distribution (L/kg) decreased concomitant with a decrease in clearance (mLlmidkg). Only Co was unrelated to body weight. The data in Table 111 was correlated with body weight according to the allometric equation PK = aBb.The resulting coefficients, exponents, and correlation coefficients are given in Table IV. For all three macrolides, the logarithm of Vd,, correlated well with the logarithm of the body weight (r > 0.97) to give slopes between 0.64 and 0.75 (Fig. 1). The
logarithm of clearance (Fig. 2) and the logarithm of the halflife (Fig. 3) also correlated well with the logarithm of the body weight (r > 0.97). The slopes and intercepts for the clearance correlations were similar for the three drugs (Table IV). Only for the half-life data, where tylosin showed a lower intercept, were there any apparent differences in the correlations. For purposes of extrapolation to human pharmacokinetics, allometric coefficients and exponents were determined from animal data alone and incorporated into the allometric equation. Table V compares the calculated pharmacokinetics to the observed human values. For erythromycin, Vd,, and clearance were 20-30% higher than the reported values and the terminal half-life was similar to the actual v a l ~ e . z For ~-~~ oleandomycin, Vd,, was -50% higher than the reported value, clearance was similar to the reported value, and terminal half-life was overestimated by about twofold. No comparisons were made for tylosin since human data was lacking.
Discussion Reports on the disposition of erythromycin, oleandmycin, and tylosin have noted biphasic kinetic^,^^.^^^^ wide tissue distribution,6,9 and rapid biliary excretion.2.8 The data presented here are consistent with these observations. Only for the 16-membered ring tylosin administered t o rats were monoexponential kinetics noted. Intraspecies values of Vd,, and clearance showed no consistent variations. For example, oleandomycin had the lowest clearance of the three macroErythromycin
-/A
Cow
Table Il-Pharmacokinetics of Oleandomycin (Mouse, Rat, and Dog) and Tylosin (Rat) After an Intravenous Dose
Oleandornycin
Tylosin
Mouse
Rat
Dog
Rat
(10 mg/kg)
(25 mg/kg)
(10 mg/kg)
(25 mg/kg)
7.4 56 6.8 51
20 92 1.6 12
11 24 2.2 86
Kinetic Parameters Co (f4mL) a
tln (min) Vdss (Ukg) CL (mUmin/kg)
9.7 42 4.8 86
Body Weight, 9
~
a
Serum concentration immediately after intravenous bolus injection.
Table Ill-Mean
Species Mouse Rat Rabbit Dog
Human cow
Figure 1-Volume of distribution of eryfhromycin, oleandomycin, and tylosin in mammals as a function of body weight. Key: (0)erythromycin; (A)oleandomycin; (0) tylosin.
Volume of Distribution and Mean Clearance Rates for Erythromycin, Oleandomycin, and Tylosin in Several Species
Body Weight,
Hepatic Blood Flow Rate,
kg
mUmina
0.02 0.25 3.2 10 0 70 0 590
1.8 17 167 434 1780 1 1060
Erythromycin Us 0.09 2.1 22 27 62 230
Oleandomycin
'
CL
tl,2
1.7 16 171 210 492 1700
39 76 84 103 131 190
Tylosin
VdS,
CL
ti 12
Vdss
CL
0.1 1 1.7
1.9 13.9
42 56
0.9
24
24
"
199
54
4602
97
16 54g
122 637
92 63
22 307
'Ref 15. bVolume of distribution at steady state (in L). 'Ref. 23. dRef.8. eClearance (in mumin). 'Half-life (in min). gRef. 7 "Ref. 26. 944
/Journal of Pharmaceutical Sciences Vol. 74, No. 9, September 1985
tl/2
I
0
I
Table IV-Allometric Parameters Describing the lnterspecies Relationshipsfor Volume of Distribution, Clearance, and Half-life'
Erythromycin
Oleandomycin
a
a
b
r
b
r
Tylosin a
b
r
Volume of 0.023 0.73 0.971 0.027 0.64 0.967 0.017 0.75 0.997 distribution Clearance 0.27 0.69 0.971 0.14 0.76 0.994 0.50 0.68 0.997 Half-life 27.7 0.14 0.973 35.5 0.14 0.998 9.1 0.18 0.992
Rabbit O H D o g
a Parameters for the allometric equation PK = aBbwhere PK is the pharmacokinetic parameter of volume of distribution (in L), clearance (in mumin), or half-life(in min), a is the empirically determined coefficient, B is the body weight (in g), and bis the empirically determined exponent. The term r is the linear correlation coefficient for the plot of the logarithm of the pharmacokinetic values versus the logarithm of body weight.
7
Erythromcyin
Mouse 10'
10
10'
10'
10'
10'
Table V-Comparison of Calculated and Observed Pharmacokineticsof Erythromycin and Oleandomycin in Humans
Body Weight, g
Figure 2-Systemic clearance rates of erythromycin, oleandomycin, and fylosin in mammals as a funcfion of body weight. Key: (0) erythromycin; (A)oleandomycin; (0)fylosin.
150
ra Vd (L)
0.970
Cl(mUmin) 0.968 ti,* (min) 0.970
-
Oleandomycin
Predicted Observed 88 662 137
62 492 132
ra 0.986 0.986 0.998
Predicted Observed 83 589 121
54 637 63
a Linear regression coefficient for the log-plot of the pharmacokinetic parameter as a function of body weight.
120 -
90
Erythromycin
-
C ._
10
10'
10'
10'
105
10'
Body Weight, g
Flgure 3- Terminal half-life of erythromycin,oleandomycin, and tylosin in mammals as a function of body weight. Key: (0)erythromycin; (A) oleandomycin; (0)fylosin.
lides in both rats and dogs, yet its clearance in humans was higher than that of erythromycin. Such intraspecies differences altered the relative pharmacokinetic ranking of these compounds so that extrapolations from any one species to humans could not be made. Only in the case of half-life was there a consistent relationship among the three antibiotics, with erythromycin having the longest half-life in the rat, rabbit, dog, human, and cow. In the absence of a n adequate animal model for macrolide antibiotics, the allometric model was used to establish an empirical relationship between the pharmacokinetic parameters of macrolides and body weight. In general, the exponents for clearance (Table IV) determined by this power fit approximated the exponential value of 0.75 derived from the similarity theory.Z7 The scaling of metabolic functions to body weight to the three-fourths power has been noted for drug clearance28.29 and is consistent with active biliary and urinary excretion processes. On the other hand, volume of distribution, although a theoretical parameter with no readily identifiable physiological correlate, should be a unit function of body weight. Reported exponential values of greater J ~ ,expo~~ than 0.9 are consistent with this r e a s ~ n i n g . l ~The nential values for volume of distribution reported here were unexpectedly low, and this was reflected in the low exponen-
tial values for the half-life. Allometric expressions for turn,~~ the over times (i.e., half-life) cluster around 0 . 2 ~ 7whereas values presented here were 0.14-0.18. It is unclear whether these deviations from theoretical values indicate that macrolide pharmacokinetics are only fortuitously scalable to body weight or whether there is a more complex allometric relationship.3" This uncertainty exemplifies a weakness of empirical modeling of pharmacokinetic data-lack of fundamental insight into drug disposition. Power curves are well known for masking real differences in the data which can lead to interpretative oversimplification.3*~3z For example, metabolic and physiological differences in drug elimination and tissue distribution may be minimized by logarithmic transformation and consequently appear as scalable functions. Another weakness of any empirical model resides in the evaluation of linearity. Obtaining a good correlation of pharmacokinetic parameters to body weight does not prove the validity of the model. Despite the good correlation coefficients shown here (>0.97) and the agreement between the observed and predicted human pharmacokinetic values for erythromycin and oleandomycin (Table V), the allometric model did not accurately discriminate between the pharmacokinetics of these two antibiotics in humans. Therefore, a simple allometric model is too imprecise to provide a relative ranking of macrolides with similar pharmacokinetics. Rather, the value of the allometric relationship resides in predicting whether large intraspecies differences in animal pharmacokinetics will translate to meaningful differences in humans. Since the pharmacokinetic parameters of erythromycin, oleandomycin, and tylosin were well correlated to body weight, the allonietric model may be applicable to other macrolides. In this case, the pharmacokinetics in laboratory animals such as the mouse, rat, rabbit, and dog could be extrapolated to other animal species as well as humans. The theoretical estimates of clearance and volume of distribution, unavailable from studies of orally administered drug, would aid in both the design of protocols and evaluation of results of animal and human studies. Journal of Pharmaceutical Sciences / 945 Vol. 74, No. 9, September 1985
References and Notes 1. Wilson. J. T.: van Boxtel. C. J. Antibiot. Chemother. 1978,. 25.. 181. 2. Chelvan, P.; Hamiltion-Miller,J. M. T.; Brumfitt, W. Br. J . Clin. Pharmacol. 1979,8, 233-235. 3. Sabbath, L. D. J . Lab. Clin. Med. 1968, 72, 916. 4. Lee. C. C.: Anderson. R. C.: Chen. K. K. Antibiot. Annu. 19531954. 485-492. 5. Lee, ’C. C.; Anderson, R. C.; Chen, K. K. J . Pharmacol. Exp. Ther. 1956,117, 274-280. 6. Lee, C. C.; Anderson, R. C.; Chen, K. K. J . Pharmacol. Exp. Ther. 1956,117, 265-273. 7. Spitzy, K. H.; Hitzenberger, G. Antibiot. Annu. 1957, 996. 8. Baggot, J. D.; Gingerich, D. A. Res. Vet. Sci. 1976,21, 318. 9. Kazenko, A.; Sorenson, 0. J.; Wolf, L. M.; Dill, W. A,; Galbraith, M.; Glazko, A. J. Antibiot. Chemother. 1957, 7 , 410-418. 10. Austin, K. L.; Mather, L. E.; Philpot, C. R.; McDonald, P. J. Br. J . Clin. Pharmacol. 1980. 10. 273. 11. DiSanto, A. R.; Chodos, ’D.J. Antimicrob. Agents Chemother. 1981,20, 190-196. 12. Dedrick, R. L. J . Pharmacokinet. Biopharm. 1973,1,435-461. 13. Adolph, E. F. Science 1949, 109, 579. 14. Dedrick. R. L.: Bischoff. K. B.: Zaharka. D. S. Cancer Chemother. Res., Part 1 1970, 54, 95-100. 15. Boxenbadm, H. J . Pharmacokinet. Biopharm. 1980,8, 165. 16. Swabb, E. A.; Bonner, D. P. J . Pharmacokinet. Biopharm. 1983, 11, 215-223. 17. Weiss, M.; Sziegoleit, W.; Forster, W. Znt. J . Clin. Pharmacol. 1977,15,572-575.
946 /Journal of Pharmaceutical Sciences Vol. 74, No. 9, September 1985
18. Boxenbaum, H. Drug Metab. Rev. 1984,15, 1071-1121. 19. Gould, S. J. Biol. Rev. 1966,41, 587. 20. Kavanagh, K.; Dennin, L. J. in “Analytical Microbiology”; Academic Press: New York, 1963; p 289. 21. Duthu, G . S. J . Liq. Chrumatogr. 1984, 7 , 1023-1032. 22. Benet, L. Z.; Galeazzi, R. L. J . 23. Welling, P. G.; Craig, W. A. J . Pharm. Sci. 1978.6: 24. Houin, G.; Tillement, J. P.; Ha Duval. J. J . Znt. Med. Res. 1980.8. 9. 25. Hall, K. W.; Ni htingale, 0.H.: Gibaldi, M.; Nelso, E.; Bates, T. R.; DiSanto, R.V. Clin. Pharmacol. 1982,22, 321. 26. Weisel, M. K.; Powers, J. D.; Powers, T. E.; Baggot, D. Am. J . Vet. Res. 1977,38, 273. 27. Gunther, B. P uegers Arch. 1972,331, 283-293. 28. Boxenbaum, $J. Pharmacokinet. Biopharm. 1982,10,201-226. 29. Boxenbaum, H.; Murray, W.; Markin, R.; Ciraulo, D. “Pharmacokinetics and Pharmacodynamics of Psychoactive Drugs”; Marcel Dekker: N e l York, in press. 30. Boxenbaum H.: Fertie. J. B. Eur. J . Metab. Pharmacokinet. 1984.9. 177. 31. Smith, R. J. Am. J . Physiol. 1984,246, R152. 32. Harver, P. H. J . Theor. Biol. 1982,95,37-42.
1.
I.
Acknowledgments The author acknowledges the fine technical assistance of Ms. Diane Farrell and Mrs. Michelle Patsiga. I wish to thank Dr. A. R. En lish for supplying the mouse data and Drs. Robert Ronfeld and H. oxenbaum for their helpful discussions.
B
differences in the pharmacokineticsof macrolide antibiotics, the disposition of erythromycin, oleandomycin, and tylosin in several mammalian species was examined. Generally, the serum concentration versus time profiles of these drugs after intravenous administration were described by two-compartment kinetic models and were similar within each species. These drugs were rapidly cleared, resulting in terminal halflives of <2 h. Comparison of their pharmacokinetics showed greater variation in antibiotic disposition among animal species than noted for the differences within a species. When the pharmacokinetic data was fitted to an allometric model, the logarithms of volume of distribution, clearance, and half-life were linearly related to the logarithms of body weight. From these relationships, the human pharmacokinetics of erythromycin and oleandomycinwere extrapolated and found to approximate observed human pharmacokinetics.
The disposition of erythromycin, the most frequently prescribed macrolide antibiotic used in the treatment of infections, has been well studied in humans,' whereas the disposition of other macrolides has been less well characterized. In humans, erythromycin is widely distributed in tissues1 and actively cleared by the liverZwith only 10-15% of the drug excreted by the kidney^.^ The disposition of macrolides in animals appear to be similar in that wide tissue distribution and biliary excretion have been rep0rted.M However, there are few comparative studies of the pharmacokinetics of erythromycin and related macrolides.7-9 Furthermore, interpretation of these studies has been complicated by the gastric instability, variable absorption, and variable protein binding of these drugs.10.11 Three macrolide antibiotics were chosen for this comparative study: the 14-membered ring antibiotics erythromycin and oleandomycin and the 16-membered ring antibiotic tylosin. The intraspecies and interspecies differences in pharmacokinetics were determined for these compounds in several animal species. Interspecies differences in pharmacokinetics are due to physical processes (such as blood flow and organ clearances) and metabolic processes.12 The physical processes can vary predictably among mammalian species, independent of metabolic processes.13 When interspecies differences in pharmacokinetics are treated as a function of body size,lPl7 species differences in drug metabolism are ignored and instead empirical scaling functions are used.18 Not only has no single species been able to predict the pharmacokinetics of macrolides in humans but the relative ranking of macrolides based on these parameters is species dependent. In an effort to more accurately estimate human pharmacokinetics from animal data, the allometric mode119 was used. The results suggest that the allometric model may be a valid part of the methodological paradigm for the prediction of human pharmacokinetics of macrolide antibiotics.
Experimental Section Intravenous Protocol-Macrolide antibiotics were administered intravenously to animals, and blood samples were collected at OO22-3~9/85/0900-0943$0 1.OO/O 0 1985, American Pharmaceutical Association
Accepted for publication May 10, 1985.
appropriate times. Male mice were dosed with erythromycin or oleandomycin at 10 mglkg. Two animals per time point were sacrificed at 0, 1,3,5, 10, 15,30,60,90,and 120 min postdose. Blood was collected and serum was prepared; the serum was assayed for the drug by microbiological assay.20 Male Sprague-Dawley rats were dosed a t 25 m g k g with erythromycin, oleandomycin,. or tylosin. Blood samples were drawn from the orbital sinus at 0,0.25,0.5,1,2, 4,and 6 h postdose. Serum was prepared and analyzed for the drug by an HPLC procedure.21 Male New Zealand White rabbits were dosed at 10 mg/kg with erythromycin. Blood was collected from the ear vein at 0, 0.25,0.5, 1, 2, 4,and 6 h postdose and serum was prepared; the serum was analyzed for the drug by HPLC. Male and female beagle dogs were dosed at 10 mglkg with erythromycin or oleandomycin; blood was drawn from the jugular vein at 0,0.25,0.5, and 24 h postdose. Serum was prepared and analyzed for 1,2,3,4,6, the drug by HPLC. Pharmacokinetic Analysis-Serum concentrations of drug were analyzed by model-independent and model-dependent pharmacokinetic methods. The area under the serum concentration versus time curve from time zero to infinity (AUC) was calculated by the trapezoidal method for AUCo-,, and by adding the extrapolated area from time t to infinity (drug concentration at tlterminal slope). The area under the first moment of the serum concentration versus time curve (AUMC)was used to calculate volume of distribution at steady state (Vd,,) according to the equation:22
Vd,,
=
(dose x AUMC)/AUC2
The terminal half-life was obtained from the log-linear leastsquares fit of the terminal portion of the serum concentration versus time curves (2-4 data points). Systemic clearance was determined by clearance = doselAUC. For compartmental analysis and estimates of initial serum concentrations (Co),the serum concentration data was fitted by computer using NONLIN. Allometric Analysis-The volume of distribution, clearance, and terminal half-life (pharmacokinetic parameters, PK) were logarithmically transformed and plotted as a function of the logarithm of the body weight. The data from the linear regression analysis was used in the allometric equation PK = aBb,where a is the y-intercept, B is the body weight in grams, and b is the slope of the log-log plot.'* The empirically determined coefficients and exponents were used t o estimate human pharmacokinetic parameters. A body weight of 7 x lo4 g was used for the human body weight.
Results The pharmacokinetic parameters which describe the kinetics of erythromycin in mice, rats, rabbits, and dogs are presented in Table I. Erythromycin showed a biphasic exponential decline in serum concentrations. The Vd,, ranged Table I-Pharmacokinetics of Erythromycin After an Intravenous Dose to Mice, Rats, Rabbits, and Dogs
Mouse
Rat
Rabbit
Dog
(10 mg/kg)
(25mg/kg)
(10 mg/kg)
(10 mg/kg)
7.8 39 3.6 77
3.5 76 9.3 73
2.5 84 6.8 53
10.6 103 2.7 21
Kinetic Parameter
Gl (MlmL)B t,, (min) vd, (Ukg)
CL (mUmin/kg) a
Serum concentration immediately after intravenous bolus injection. Journal of Pharmaceutical Sciences 1943 Vol. 74, No. 9, September 1985
from 2.7 to 9.3 L/kg and the half-life increased, while clearance decreased with increasing species body weight. Dogs had the highest initial serum concentration of drug (CO) after intravenous dosing. Like erythromycin, oleandomycin exhibited biphasic kinetics with similar relationships among the pharmacokinetic parameters (Table 11): Vd,, was 1.6-6.8 L/kg and clearance rates decreased and terminal half-lives increased with increasing species body weight. The dog was again notable for high Co values. Tylosin, in contrast to erythromycin and oleandomycin, decreased monoexponentially in the rat, with the shortest half-life, highest clearance rate, and smallest Vd,, of the three macrolides in the rat (Table 11). Table I11 summarizes the pharmacokinetic data reported in the literature or by this laboratory for erythromycin, oleandomycin, and tylosin. Large volumes of distribution (greater than the body volume) were observed for all three macrolides in the dog and smaller species; for humans and cows, the Vd,, values were less than their respective body volumes. Clearance rates for the three macrolides were comparable to hepatic blood flow in the mouse, rat, and rabbit but were considerably lower in the dog, human, and cow. The three smaller animal species also had shorter terminal half-lives (<2 h). Differences in the volumes of distribution, clearances, and half-lives within a n animal species for the three antibiotics (intraspecies differences) and differences across species for each antibiotic (interspecies differences) were compared. The intraspecies differences were less than threefold, whereas the interspecies differences varied as much as 10-fold (Table 111).The interspecies differences appeared to be generally related to body weight: as body weight increased, the terminal half-life increased and the volume of distribution (L/kg) decreased concomitant with a decrease in clearance (mLlmidkg). Only Co was unrelated to body weight. The data in Table 111 was correlated with body weight according to the allometric equation PK = aBb.The resulting coefficients, exponents, and correlation coefficients are given in Table IV. For all three macrolides, the logarithm of Vd,, correlated well with the logarithm of the body weight (r > 0.97) to give slopes between 0.64 and 0.75 (Fig. 1). The
logarithm of clearance (Fig. 2) and the logarithm of the halflife (Fig. 3) also correlated well with the logarithm of the body weight (r > 0.97). The slopes and intercepts for the clearance correlations were similar for the three drugs (Table IV). Only for the half-life data, where tylosin showed a lower intercept, were there any apparent differences in the correlations. For purposes of extrapolation to human pharmacokinetics, allometric coefficients and exponents were determined from animal data alone and incorporated into the allometric equation. Table V compares the calculated pharmacokinetics to the observed human values. For erythromycin, Vd,, and clearance were 20-30% higher than the reported values and the terminal half-life was similar to the actual v a l ~ e . z For ~-~~ oleandomycin, Vd,, was -50% higher than the reported value, clearance was similar to the reported value, and terminal half-life was overestimated by about twofold. No comparisons were made for tylosin since human data was lacking.
Discussion Reports on the disposition of erythromycin, oleandmycin, and tylosin have noted biphasic kinetic^,^^.^^^^ wide tissue distribution,6,9 and rapid biliary excretion.2.8 The data presented here are consistent with these observations. Only for the 16-membered ring tylosin administered t o rats were monoexponential kinetics noted. Intraspecies values of Vd,, and clearance showed no consistent variations. For example, oleandomycin had the lowest clearance of the three macroErythromycin
-/A
Cow
Table Il-Pharmacokinetics of Oleandomycin (Mouse, Rat, and Dog) and Tylosin (Rat) After an Intravenous Dose
Oleandornycin
Tylosin
Mouse
Rat
Dog
Rat
(10 mg/kg)
(25 mg/kg)
(10 mg/kg)
(25 mg/kg)
7.4 56 6.8 51
20 92 1.6 12
11 24 2.2 86
Kinetic Parameters Co (f4mL) a
tln (min) Vdss (Ukg) CL (mUmin/kg)
9.7 42 4.8 86
Body Weight, 9
~
a
Serum concentration immediately after intravenous bolus injection.
Table Ill-Mean
Species Mouse Rat Rabbit Dog
Human cow
Figure 1-Volume of distribution of eryfhromycin, oleandomycin, and tylosin in mammals as a function of body weight. Key: (0)erythromycin; (A)oleandomycin; (0) tylosin.
Volume of Distribution and Mean Clearance Rates for Erythromycin, Oleandomycin, and Tylosin in Several Species
Body Weight,
Hepatic Blood Flow Rate,
kg
mUmina
0.02 0.25 3.2 10 0 70 0 590
1.8 17 167 434 1780 1 1060
Erythromycin Us 0.09 2.1 22 27 62 230
Oleandomycin
'
CL
tl,2
1.7 16 171 210 492 1700
39 76 84 103 131 190
Tylosin
VdS,
CL
ti 12
Vdss
CL
0.1 1 1.7
1.9 13.9
42 56
0.9
24
24
"
199
54
4602
97
16 54g
122 637
92 63
22 307
'Ref 15. bVolume of distribution at steady state (in L). 'Ref. 23. dRef.8. eClearance (in mumin). 'Half-life (in min). gRef. 7 "Ref. 26. 944
/Journal of Pharmaceutical Sciences Vol. 74, No. 9, September 1985
tl/2
I
0
I
Table IV-Allometric Parameters Describing the lnterspecies Relationshipsfor Volume of Distribution, Clearance, and Half-life'
Erythromycin
Oleandomycin
a
a
b
r
b
r
Tylosin a
b
r
Volume of 0.023 0.73 0.971 0.027 0.64 0.967 0.017 0.75 0.997 distribution Clearance 0.27 0.69 0.971 0.14 0.76 0.994 0.50 0.68 0.997 Half-life 27.7 0.14 0.973 35.5 0.14 0.998 9.1 0.18 0.992
Rabbit O H D o g
a Parameters for the allometric equation PK = aBbwhere PK is the pharmacokinetic parameter of volume of distribution (in L), clearance (in mumin), or half-life(in min), a is the empirically determined coefficient, B is the body weight (in g), and bis the empirically determined exponent. The term r is the linear correlation coefficient for the plot of the logarithm of the pharmacokinetic values versus the logarithm of body weight.
7
Erythromcyin
Mouse 10'
10
10'
10'
10'
10'
Table V-Comparison of Calculated and Observed Pharmacokineticsof Erythromycin and Oleandomycin in Humans
Body Weight, g
Figure 2-Systemic clearance rates of erythromycin, oleandomycin, and fylosin in mammals as a funcfion of body weight. Key: (0) erythromycin; (A)oleandomycin; (0)fylosin.
150
ra Vd (L)
0.970
Cl(mUmin) 0.968 ti,* (min) 0.970
-
Oleandomycin
Predicted Observed 88 662 137
62 492 132
ra 0.986 0.986 0.998
Predicted Observed 83 589 121
54 637 63
a Linear regression coefficient for the log-plot of the pharmacokinetic parameter as a function of body weight.
120 -
90
Erythromycin
-
C ._
10
10'
10'
10'
105
10'
Body Weight, g
Flgure 3- Terminal half-life of erythromycin,oleandomycin, and tylosin in mammals as a function of body weight. Key: (0)erythromycin; (A) oleandomycin; (0)fylosin.
lides in both rats and dogs, yet its clearance in humans was higher than that of erythromycin. Such intraspecies differences altered the relative pharmacokinetic ranking of these compounds so that extrapolations from any one species to humans could not be made. Only in the case of half-life was there a consistent relationship among the three antibiotics, with erythromycin having the longest half-life in the rat, rabbit, dog, human, and cow. In the absence of a n adequate animal model for macrolide antibiotics, the allometric model was used to establish an empirical relationship between the pharmacokinetic parameters of macrolides and body weight. In general, the exponents for clearance (Table IV) determined by this power fit approximated the exponential value of 0.75 derived from the similarity theory.Z7 The scaling of metabolic functions to body weight to the three-fourths power has been noted for drug clearance28.29 and is consistent with active biliary and urinary excretion processes. On the other hand, volume of distribution, although a theoretical parameter with no readily identifiable physiological correlate, should be a unit function of body weight. Reported exponential values of greater J ~ ,expo~~ than 0.9 are consistent with this r e a s ~ n i n g . l ~The nential values for volume of distribution reported here were unexpectedly low, and this was reflected in the low exponen-
tial values for the half-life. Allometric expressions for turn,~~ the over times (i.e., half-life) cluster around 0 . 2 ~ 7whereas values presented here were 0.14-0.18. It is unclear whether these deviations from theoretical values indicate that macrolide pharmacokinetics are only fortuitously scalable to body weight or whether there is a more complex allometric relationship.3" This uncertainty exemplifies a weakness of empirical modeling of pharmacokinetic data-lack of fundamental insight into drug disposition. Power curves are well known for masking real differences in the data which can lead to interpretative oversimplification.3*~3z For example, metabolic and physiological differences in drug elimination and tissue distribution may be minimized by logarithmic transformation and consequently appear as scalable functions. Another weakness of any empirical model resides in the evaluation of linearity. Obtaining a good correlation of pharmacokinetic parameters to body weight does not prove the validity of the model. Despite the good correlation coefficients shown here (>0.97) and the agreement between the observed and predicted human pharmacokinetic values for erythromycin and oleandomycin (Table V), the allometric model did not accurately discriminate between the pharmacokinetics of these two antibiotics in humans. Therefore, a simple allometric model is too imprecise to provide a relative ranking of macrolides with similar pharmacokinetics. Rather, the value of the allometric relationship resides in predicting whether large intraspecies differences in animal pharmacokinetics will translate to meaningful differences in humans. Since the pharmacokinetic parameters of erythromycin, oleandomycin, and tylosin were well correlated to body weight, the allonietric model may be applicable to other macrolides. In this case, the pharmacokinetics in laboratory animals such as the mouse, rat, rabbit, and dog could be extrapolated to other animal species as well as humans. The theoretical estimates of clearance and volume of distribution, unavailable from studies of orally administered drug, would aid in both the design of protocols and evaluation of results of animal and human studies. Journal of Pharmaceutical Sciences / 945 Vol. 74, No. 9, September 1985
References and Notes 1. Wilson. J. T.: van Boxtel. C. J. Antibiot. Chemother. 1978,. 25.. 181. 2. Chelvan, P.; Hamiltion-Miller,J. M. T.; Brumfitt, W. Br. J . Clin. Pharmacol. 1979,8, 233-235. 3. Sabbath, L. D. J . Lab. Clin. Med. 1968, 72, 916. 4. Lee. C. C.: Anderson. R. C.: Chen. K. K. Antibiot. Annu. 19531954. 485-492. 5. Lee, ’C. C.; Anderson, R. C.; Chen, K. K. J . Pharmacol. Exp. Ther. 1956,117, 274-280. 6. Lee, C. C.; Anderson, R. C.; Chen, K. K. J . Pharmacol. Exp. Ther. 1956,117, 265-273. 7. Spitzy, K. H.; Hitzenberger, G. Antibiot. Annu. 1957, 996. 8. Baggot, J. D.; Gingerich, D. A. Res. Vet. Sci. 1976,21, 318. 9. Kazenko, A.; Sorenson, 0. J.; Wolf, L. M.; Dill, W. A,; Galbraith, M.; Glazko, A. J. Antibiot. Chemother. 1957, 7 , 410-418. 10. Austin, K. L.; Mather, L. E.; Philpot, C. R.; McDonald, P. J. Br. J . Clin. Pharmacol. 1980. 10. 273. 11. DiSanto, A. R.; Chodos, ’D.J. Antimicrob. Agents Chemother. 1981,20, 190-196. 12. Dedrick, R. L. J . Pharmacokinet. Biopharm. 1973,1,435-461. 13. Adolph, E. F. Science 1949, 109, 579. 14. Dedrick. R. L.: Bischoff. K. B.: Zaharka. D. S. Cancer Chemother. Res., Part 1 1970, 54, 95-100. 15. Boxenbadm, H. J . Pharmacokinet. Biopharm. 1980,8, 165. 16. Swabb, E. A.; Bonner, D. P. J . Pharmacokinet. Biopharm. 1983, 11, 215-223. 17. Weiss, M.; Sziegoleit, W.; Forster, W. Znt. J . Clin. Pharmacol. 1977,15,572-575.
946 /Journal of Pharmaceutical Sciences Vol. 74, No. 9, September 1985
18. Boxenbaum, H. Drug Metab. Rev. 1984,15, 1071-1121. 19. Gould, S. J. Biol. Rev. 1966,41, 587. 20. Kavanagh, K.; Dennin, L. J. in “Analytical Microbiology”; Academic Press: New York, 1963; p 289. 21. Duthu, G . S. J . Liq. Chrumatogr. 1984, 7 , 1023-1032. 22. Benet, L. Z.; Galeazzi, R. L. J . 23. Welling, P. G.; Craig, W. A. J . Pharm. Sci. 1978.6: 24. Houin, G.; Tillement, J. P.; Ha Duval. J. J . Znt. Med. Res. 1980.8. 9. 25. Hall, K. W.; Ni htingale, 0.H.: Gibaldi, M.; Nelso, E.; Bates, T. R.; DiSanto, R.V. Clin. Pharmacol. 1982,22, 321. 26. Weisel, M. K.; Powers, J. D.; Powers, T. E.; Baggot, D. Am. J . Vet. Res. 1977,38, 273. 27. Gunther, B. P uegers Arch. 1972,331, 283-293. 28. Boxenbaum, $J. Pharmacokinet. Biopharm. 1982,10,201-226. 29. Boxenbaum, H.; Murray, W.; Markin, R.; Ciraulo, D. “Pharmacokinetics and Pharmacodynamics of Psychoactive Drugs”; Marcel Dekker: N e l York, in press. 30. Boxenbaum H.: Fertie. J. B. Eur. J . Metab. Pharmacokinet. 1984.9. 177. 31. Smith, R. J. Am. J . Physiol. 1984,246, R152. 32. Harver, P. H. J . Theor. Biol. 1982,95,37-42.
1.
I.
Acknowledgments The author acknowledges the fine technical assistance of Ms. Diane Farrell and Mrs. Michelle Patsiga. I wish to thank Dr. A. R. En lish for supplying the mouse data and Drs. Robert Ronfeld and H. oxenbaum for their helpful discussions.
B